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Contents
I. A Library of Elementary Functions
1. Linear Equations and Graphs
1.1 Linear Equations and Inequalities
1.2 Graphs and Lines
1.3 Linear Regression
Chapter 1 Summary and Review
Review Exercises
2. Functions and Graphs
2.1 Functions
2.2 Elementary Functions: Graphs and Transformations
2.3 Quadratic Functions
2.4 Polynomial and Rational Functions
2.5 Exponential Functions
2.6 Logarithmic Functions
Chapter 2 Summary and Review
Review Exercises
II. Finite Mathematics
3. Mathematics of Finance
3.1 Simple Interest
3.2 Compound and Continuous Compound Interest
3.3 Future Value of an Annuity; Sinking Funds
3.4 Present Value of an Annuity; Amortization
Chapter 3 Summary and Review
Review Exercises
4. Systems of Linear Equations; Matrices
4.1 Review: Systems of Linear Equations in Two Variables
4.2 Systems of Linear Equations and Augmented Matrices
4.3 Gauss - Jordan Elimination
4.4 Matrices: Basic Operations
4.5 Inverse of a Square Matrix
4.6 Matrix Equations and Systems of Linear Equations
4.7 Leontief Input - Output Analysis
Chapter 4 Summary and Review
Review Exercises
5. Linear Inequalities and Linear Programming
5.1 Linear Inequalities in Two Variables
5.2 Systems of Linear Inequalities in Two Variables
5.3 Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Summary and Review
Review Exercises
6. Linear Programming: The Simplex Method
6.1 The Table Method: An Introduction to the Simplex Method
6.2 The Simplex Method: Maximization with Problem Constraints of the Form ≤
6.3 The Dual Problem: Minimization with Problem Constraints of the Form ≥
6.4 Maximization and Minimization with Mixed Problem Constraints
Chapter 6 Summary and Review
Review Exercises
7. Logic, Sets, and Counting
7.1 Logic
7.2 Sets
7.3 Basic Counting Principles
7.4 Permutations and Combinations
Chapter 7 Summary and Review
Review Exercises
8. Probability
8.1 Sample Spaces, Events, and Probability
8.2 Union, Intersection, and Complement of Events; Odds
8.3 Conditional Probability, Intersection, and Independence
8.4 Bayes' Formula
8.5 Random Variable, Probability Distribution, and Expected Value
Chapter 8 Summary and Review
Review Exercises
III. Calculus
9. Limits and the Derivative
9.1 Introduction to Limits
9.2 Infinite Limits and Limits at Infinity
9.3 Continuity
9.4 The Derivative
9.5 Basic Differentiation Properties
9.6 Differentials
9.7 Marginal Analysis in Business and Economics
Chapter 9 Summary and Review
Review Exercises
10. Additional Derivative Topics
10.1 The Constant e and Continuous Compound Interest
10.2 Derivatives of Exponential and Logarithmic Functions
10.3 Derivatives of Products and Quotients
10.4 The Chain Rule
10.5 Implicit Differentiation
10.6 Related Rates
10.7 Elasticity of Demand
Chapter 10 Summary and Review
Review Exercises
11. Graphing and Optimization
11.1 First Derivative and Graphs
11.2 Second Derivative and Graphs
11.3 L'Hôpital's Rule
11.4 Curve-Sketching Techniques
11.5 Absolute Maxima and Minima
11.6 Optimization
Chapter 11 Summary and Review
Review Exercises
12. Integration
12.1 Antiderivatives and Indefinite Integrals
12.2 Integration by Substitution
12.3 Differential Equations; Growth and Decay
12.4 The Definite Integral
12.5 The Fundamental Theorem of Calculus
Chapter 12 Summary and Review
Review Exercises
13. Additional Integration Topics
13.1 Area Between Curves
13.2 Applications in Business and Economics
13.3 Integration by Parts
13.4 Other Integration Methods
Chapter 13 Summary and Review
Review Exercises
14. Multivariable Calculus
14.1 Functions of Several Variables
14.2 Partial Derivatives
14.3 Maxima and Minima
14.4 Maxima and Minima Using Lagrange Multipliers
14.5 Method of Least Squares
14.6 Double Integrals over Rectangular Regions
14.7 Double Integrals over More General Regions
Chapter 14 Summary and Review
Review Exercises
15. Markov Chains (online at goo.gl/8SZkyn)
15.1 Properties of Markov Chains
15.2 Regular Markov Chains
15.3 Absorbing Markov Chains
Chapter 15 Summary and Review
Review Exercises
Appendix A: Basic Algebra Review
A.1 Real Numbers
A.2 Operations on Polynomials
A.3 Factoring Polynomials
A.4 Operations on Rational Expressions
A.5 Integer Exponents and Scientific Notation
A.6 Rational Exponents and Radicals
A.7 Quadratic Equations
Appendix B: Special Topics (online at goo.gl/mjbXrG)
B.1 Sequences, Series, and Summation Notation
B.2 Arithmetic and Geometric Sequences
B.3 Binomial Theorem
B.4 Interpolating Polynomials and Divided Differences
Appendix C: Tables
Table I Integration Formulas
Table II Area under the Standard Normal Curve
Answers Index Index of Applications
